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An Algorithm to Solve the Discrete Logarithm Problem with the Number Field Sieve
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1002/0471667196.ess1558openalex-snapshot
Mathematics of Computation
inferredcites →https://doi.org/10.1007/3-540-39757-4_20openalex-snapshot
Discrete logarithms in finite fields and their cryptographic significance
inferredcites →https://doi.org/10.1007/978-1-4612-4808-8openalex-snapshot
Open Problems in Communication and Computation
inferredcites →https://doi.org/10.1007/978-1-4612-4808-8_29openalex-snapshot
The Complexity of Computing Discrete Logarithms and Factoring Integers
inferredcites →https://doi.org/10.1007/978-3-0348-8295-8openalex-snapshot
Cryptography and Computational Number Theory
inferredcites →https://doi.org/10.1007/bf00198464openalex-snapshot
Modifications to the Number Field Sieve
inferredcites →https://doi.org/10.1007/bfb0091534openalex-snapshot
The development of the number field sieve
inferredcites →https://doi.org/10.1007/bfb0091541openalex-snapshot
A general number field sieve implementation
inferredcites →https://doi.org/10.1007/pl00003816openalex-snapshot
Parallel Collision Search with Cryptanalytic Applications
inferredcites →https://doi.org/10.1016/0022-314x(83)90002-1openalex-snapshot
On a problem of Oppenheim concerning “factorisatio numerorum”
inferredcites →https://doi.org/10.1016/b978-0-12-386870-1.50014-9openalex-snapshot
Fast, Rigorous Factorization and Discrete Logarithm Algorithms
inferredcites →https://doi.org/10.1023/a:1008350005447openalex-snapshot
Discrete Logarithms: The Past and the Future
inferredcites →https://doi.org/10.1090/conm/168openalex-snapshot
Finite Fields: Theory, Applications, and Algorithms
inferredcites →https://doi.org/10.1090/conm/168/01706openalex-snapshot
Discrete logarithms and smooth polynomials
inferredcites →https://doi.org/10.1090/psapm/042/1095551openalex-snapshot
The discrete logarithm problem
inferredcites →https://doi.org/10.1090/s0025-5718-00-01308-9openalex-snapshot
Special prime numbers and discrete logs in finite prime fields
inferredcites →https://doi.org/10.1090/s0025-5718-02-01482-5openalex-snapshot
Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the gaussian integer method
inferredcites →https://doi.org/10.1090/s0025-5718-1978-0491431-9openalex-snapshot
Monte Carlo methods for index computation (𝑚𝑜𝑑𝑝)
inferredcites →https://doi.org/10.1090/s0025-5718-1992-1106981-9openalex-snapshot
Searching for primitive roots in finite fields
inferredcites →https://doi.org/10.1098/rsta.1993.0139openalex-snapshot
Discrete logarithms and local units
inferredcites →https://doi.org/10.1109/tit.1984.1056941openalex-snapshot
Fast evaluation of logarithms in fields of characteristic two
inferredcites →https://doi.org/10.1109/tit.1986.1057137openalex-snapshot
Solving sparse linear equations over finite fields
inferredcites →https://doi.org/10.1137/0406010openalex-snapshot
Discrete Logarithms in $GF ( P )$ Using the Number Field Sieve
inferredcites →https://doi.org/10.1515/156939203321669546openalex-snapshot
On asymptotic complexity of computing discrete logarithms over GF(p)
inferredcites →https://doi.org/10.2307/1971363openalex-snapshot
Factoring Integers with Elliptic Curves
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
inferred← citeshttps://doi.org/10.1002/spy2.234openalex-snapshot
An initial step toward a quantum annealing approach to the discrete logarithm problem
inferred← citeshttps://doi.org/10.1007/978-1-4419-5906-5_834openalex-snapshot
Number Field Sieve for the DLP
inferred← citeshttps://doi.org/10.1007/978-3-031-91829-2_5openalex-snapshot
Intermundium-DL: Assessing the Resilience of Current Schemes to Discrete-Log-Computation Attacks on Public Parameters
inferred← citeshttps://doi.org/10.1007/978-3-319-56620-7_8openalex-snapshot
A Kilobit Hidden SNFS Discrete Logarithm Computation
inferred← citeshttps://doi.org/10.1007/978-3-319-69453-5_30openalex-snapshot
Solving Discrete Logarithms on a 170-Bit MNT Curve by Pairing Reduction
inferred← citeshttps://doi.org/10.1007/978-3-540-76900-2_2openalex-snapshot
When e-th Roots Become Easier Than Factoring
inferred← citeshttps://doi.org/10.1007/978-3-642-42001-6_8openalex-snapshot
An Experiment of Number Field Sieve for Discrete Logarithm Problem over GF(p 12)
inferred← citeshttps://doi.org/10.1007/978-3-642-42045-0_17openalex-snapshot
Non-uniform Cracks in the Concrete: The Power of Free Precomputation
inferred← citeshttps://doi.org/10.1007/978-3-662-48797-6_7openalex-snapshot
Computing Individual Discrete Logarithms Faster in $${{\mathrm{GF}}}(p^n)$$ with the NFS-DL Algorithm
inferred← citeshttps://doi.org/10.1007/978-3-662-48800-3_2openalex-snapshot
The Tower Number Field Sieve
inferred← citeshttps://doi.org/10.1007/978-3-662-53018-4_20openalex-snapshot
Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case
inferred← citeshttps://doi.org/10.1007/s00145-018-9280-5openalex-snapshot
Updating Key Size Estimations for Pairings
inferred← citeshttps://doi.org/10.1007/s10623-025-01590-3openalex-snapshot
Utilizing two subfields to accelerate individual logarithm computation in extended tower number field sieve
inferred← citeshttps://doi.org/10.1007/s10623-025-01788-5openalex-snapshot
On the complexity formulae of the number field sieve and its variants
inferred← citeshttps://doi.org/10.1016/j.tcs.2020.01.010openalex-snapshot
Refined analysis to the extended tower number field sieve
inferred← citeshttps://doi.org/10.1017/9781139049801.013openalex-snapshot
The impact of the number field sieve on the discrete logarithm problem in finite fields
inferred← citeshttps://doi.org/10.1090/mcom/3376openalex-snapshot
Faster individual discrete logarithms in finite fields of composite extension degree
inferred← citeshttps://doi.org/10.1090/s0025-5718-09-02198-xopenalex-snapshot
The number field sieve for integers of low weight
inferred← citeshttps://doi.org/10.1109/ccwc.2018.8301754openalex-snapshot
A new elliptic cryptographic algorithm
inferred← citeshttps://doi.org/10.1109/tit.2023.3244631openalex-snapshot
Constructing CM Fields for NFS to Accelerate DL Computation in Non-Prime Finite Fields
inferred← citeshttps://doi.org/10.1112/s1461157014000369openalex-snapshot
The multiple number field sieve for medium- and high-characteristic finite fields
inferred← citeshttps://doi.org/10.1112/s1461157016000164openalex-snapshot
Collecting relations for the number field sieve in
inferred← citeshttps://doi.org/10.1145/3422370openalex-snapshot
Identity-based Encryption from the Diffie-Hellman Assumption
inferred← citeshttps://doi.org/10.2478/v10127-010-0012-yopenalex-snapshot
On the use of the lattice sieve in the 3D NFS
inferred← citeshttps://doi.org/10.48550/arxiv.2005.04883openalex-snapshot
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